Question 14 Marks
If $\mathrm{m}-\frac{1}{\mathrm{~m}}=5$, find: $\mathrm{m}^2-\frac{1}{\mathrm{~m}^2}$
Answer$ \mathrm{m}^2-\frac{1}{\mathrm{~m}^2}=\left(\mathrm{m}+\frac{1}{\mathrm{~m}}\right)\left(\mathrm{m}-\frac{1}{\mathrm{~m}}\right)$
$ =5\left(\mathrm{~m}+\frac{1}{\mathrm{~m}}\right)$
$ \text { Now }\left(\mathrm{m}+\frac{1}{\mathrm{~m}}\right)^2=\left(\mathrm{m}-\frac{1}{\mathrm{~m}}\right)^2+4$
$ =(5)^2+4$
$ =25+4$
$ =29$
$ \therefore \mathrm{m}+\frac{1}{\mathrm{~m}}=\sqrt{29}$
$ \therefore \mathrm{m}^2-\frac{1}{\mathrm{~m}^2}=(5)(\sqrt{29})=5 \sqrt{29}$
View full question & answer→Question 24 Marks
The sum of the squares of two numbers is $13$ and their product is $6$. Find : $(i)$ the sum of the two numbers.$(ii)$ the difference between them.
AnswerLet $x$ and $y$ be the two numbers, then,
$x^2+y^2=13$ and $x y=6$
$(i) (x+y)^2=x^2+y^2+2 x y$
$=13+2 \times 6$
$=13+12$
$=25$
$\therefore x+y= \pm \sqrt{25}= \pm 5$
$(ii) (x-y)^2=x^2+y^2-2 x y$
$=13-12$
$=1$
$\therefore x-y= \pm 1$
View full question & answer→Question 34 Marks
If $3 x+\frac{1}{3 x}=3$, find : $27 x^3+\frac{1}{27 x^3}$
Answer$ 3 \mathrm{x}+\frac{1}{3 \mathrm{x}}=3$
$ \Rightarrow\left(3 \mathrm{x}+\frac{1}{3 \mathrm{x}}\right)^3=(3)^3$
$ \Rightarrow(3 \mathrm{x})^3+\left(\frac{1}{3 \mathrm{x}}\right)^3+3 \times 3 \mathrm{x} \times \frac{1}{3 \mathrm{x}}\left(3 \mathrm{x}+\frac{1}{3 \mathrm{x}}\right)=27$
$ \Rightarrow 27 \mathrm{x}^3+\frac{1}{27 \mathrm{x}^3}+3\left(3 \mathrm{x}+\frac{1}{3 \mathrm{x}}\right)=27$
$ \Rightarrow 27 \mathrm{x}^3+\frac{1}{27 \mathrm{x}^3}+3(3)=27$
$ \Rightarrow 27 \mathrm{x}^3+\frac{1}{27 \mathrm{x}^3}+9=27$
$ \Rightarrow 27 \mathrm{x}^3+\frac{1}{27 \mathrm{x}^3}=27-9$
$ \Rightarrow 27 \mathrm{x}^3+\frac{1}{27 \mathrm{x}^3}=18$
View full question & answer→Question 44 Marks
If $3 x+\frac{1}{3 x}=3$, find: $9 x^2+\frac{1}{9 x^2}$
Answer$ 3 x+\frac{1}{3 x}=3$
$ \Rightarrow\left(3 x+\frac{1}{3 x}\right)^2=(3)^2$
$ \Rightarrow(3 x)^2+\left(\frac{1}{3 x}\right)^2+2 \times 3 x \times \frac{1}{3 x}=9$
$ \Rightarrow 9 x^2+\frac{1}{9 x^2}+2=9$
$ \Rightarrow 9 x^2+\frac{1}{9 x^2}=9-2$
$ \Rightarrow 9 x^2+\frac{1}{9 x^2}=7$
View full question & answer→Question 54 Marks
If $2 x-\frac{1}{2 x}=4$, find : $8 x^3-\frac{1}{8 x^3}$
Answer$ 2 \mathrm{x}-\frac{1}{2 \mathrm{x}}=4$
$ \Rightarrow\left(2 \mathrm{x}-\frac{1}{2 \mathrm{x}}\right)^3=(4)^3$
$ \Rightarrow(2 \mathrm{x})^3-\left(\frac{1}{2 \mathrm{x}}\right)^3-3 \times 2 \mathrm{x} \times \frac{1}{2 \mathrm{x}}\left(2 \mathrm{x}-\frac{1}{2 \mathrm{x}}\right)=64$
$ \Rightarrow 8 \mathrm{x}^3-\frac{1}{8 \mathrm{x}^3}-3(4)=64$
$ \Rightarrow 8 \mathrm{x}^3-\frac{1}{8 \mathrm{x}^3}-12=64$
$ \Rightarrow 8 \mathrm{x}^3-\frac{1}{8 \mathrm{x}^3}=64+12$
$ \Rightarrow 8 \mathrm{x}^3-\frac{1}{8 \mathrm{x}^3}=76$
View full question & answer→Question 64 Marks
If $2 x-\frac{1}{2 x}=4$, find $: 4 x^2+\frac{1}{4 x^2}$
Answer$ 2 \mathrm{x}-\frac{1}{2 \mathrm{x}}=4$
$ \Rightarrow\left(2 \mathrm{x}-\frac{1}{2 \mathrm{x}}\right)^2=(4)^2$
$ \Rightarrow(2 \mathrm{x})^2+\left(\frac{1}{2 \mathrm{x}}\right)^2-2 \times 2 \mathrm{x} \times \frac{1}{2 \mathrm{x}}=16$
$ \Rightarrow 4 \mathrm{x}^2+\frac{1}{4 \mathrm{x}^2}-2=16$
$ \Rightarrow 4 \mathrm{x}^2+\frac{1}{4 \mathrm{x}^2}=16+2$
$ \Rightarrow 4 \mathrm{x}^2+\frac{1}{4 \mathrm{x}^2}=18$
View full question & answer→Question 74 Marks
Find: $\mathrm{a}^3-\frac{1}{\mathrm{a}^3}$, if $\mathrm{a}-\frac{1}{\mathrm{a}}=4$.
Answer$ a-\frac{1}{a}=4$
$ \Rightarrow\left(a-\frac{1}{a}\right)^3=(4)^3$
$ \Rightarrow a^3-\frac{1}{a^3}-3 a \times \frac{1}{a}\left(a-\frac{1}{a}\right)=64$
$ \Rightarrow a^3-\frac{1}{a^3}+3(4)=64 \ldots \ldots . . .\left[\because-\frac{1}{a}=4\right]$
$ \Rightarrow a^3-\frac{1}{a^3}-12=64$
$ \Rightarrow a^3-\frac{1}{a^3}=64+12$
$ \Rightarrow a^3-\frac{1}{a^3}=76$
View full question & answer→Question 84 Marks
Find: $\mathrm{a}^3+\frac{1}{\mathrm{a}^3}$, if $\mathrm{a}+\frac{1}{\mathrm{a}}=5$.
Answer$ \mathrm{a}+\frac{1}{\mathrm{a}}=5$
$ \Rightarrow\left(\mathrm{a}+\frac{1}{\mathrm{a}}\right)^3=(5)^3$
$ \Rightarrow \mathrm{a}^3+\frac{1}{\mathrm{a}^3}+3 \mathrm{a} \times \frac{1}{\mathrm{a}}\left(\mathrm{a}+\frac{1}{\mathrm{a}}\right)=125$
$ \Rightarrow \mathrm{a}^3+\frac{1}{\mathrm{a}^3}+3(5)=125 \ldots \ldots\left[\mathrm{a}+\frac{1}{\mathrm{a}}=5\right]$
$ \Rightarrow \mathrm{a}^3+\frac{1}{\mathrm{a}^3}+15=125$
$ \Rightarrow \mathrm{a}^3+\frac{1}{\mathrm{a}^3}=125-15$
$ \Rightarrow \mathrm{a}^3+\frac{1}{\mathrm{a}^3}=110$
View full question & answer→Question 94 Marks
Find : $a + b + c,$ if $a^2 + b^2 + c^2 = 83$ and $ab + bc + ca = 71.$
Answer$ (a+b+c)^2=a^2+b^2+c^2+2 a b+2 b c+2 c a$
$ \Rightarrow(a+b+c)^2=82+2(a b+b c+c a)$
$ \Rightarrow(a+b+c)^2=83+2 \times 71$
$ \Rightarrow(a+b+c)^2=83+142$
$ \Rightarrow(a+b+c)^2=225$
$ \Rightarrow a+b+c=\sqrt{225}$
$ \Rightarrow a+b+c= \pm 15$
View full question & answer→Question 104 Marks
Find : $a^2 + b^2 + c^2,$ if $a + b + c = 9$ and $ab + bc + ca = 24$
Answer$a+ b + c = 9$
$\Rightarrow (a + b + c)^2 = (9)2$
$\Rightarrow a^2 + b^2+ c^2 + 2ab + 2bc + 2ca = 81$
$\Rightarrow a^2+ b^2 + c^2+ 2(ab + bc + ca) = 81$
$\Rightarrow a^2 + b^2 + c^2+ 2\times 24 = 81$
$\Rightarrow a^2 + b^2+ c^2 + 48 = 81$
$\Rightarrow a^2 + b^2+ c^2= 81 − 48$
$\Rightarrow a^2 + b^2 + c^2 = 33$
View full question & answer→Question 114 Marks
Expand : $(6a – 7b)^3$
Answer$(6a – 7b)^3$
$= (6a)^3 – (7b)^3 – 3(6a) (7b) (6a – 7b)$
$= 216a^3 – 343b^3– 126ab (6a – 7b)$
$= 216a^3 – 343b^3 – 756a^2b + 882ab^2$
$= 216a^3 – 756a^2b + 882ab^2 – 343b^3$
View full question & answer→Question 124 Marks
Expand : $(5x + 3y)^3$
Answer$(5x + 3y)^3$
$= (5x)^3 + (3y)^3 + 3 (5x) (3y) (5x + 3y)$
$= 125x^3 + 27y^3 + 45xy (5x + 3y)$
$= 125x^3+ 27y^3+ 225x^2y + 135xy^2$
View full question & answer→Question 134 Marks
Expand : $(2a – 5b – 4c)^2$
Answer$(2a – 5b – 4c)^2$
$= (2a)^2 + (–5b)^2 + (–4c)^2 + 2 (2a) (–5b) + 2 (–5b) (–4c) + 2 (–4c) (2a)$
$= 4a^2 + 25b^2 + 16c^2 – 20ab + 40bc – 16ca$
View full question & answer→Question 144 Marks
Expand : $(3x – 4y + 5z)^2$
Answer$(3x – 4y + 5z)^2$
$= (3x)^2+ (– 4y)^2 + (5z)^2+ 2(3x) (– 4y) + 2(– 4y) (5z) + 2(5z) (3x)$
$= 9x^2 + 16y^2 + 25z^2 – 24xy – 40yz + 30zx$
View full question & answer→Question 154 Marks
If $3 x-\frac{1}{3 x}=5$, find : $81 x^4+\frac{1}{81 x^4}$
Answer$81 x^4+\frac{1}{81 x^4}$
$=\left(9 x^2+\frac{1}{9 x^2}\right)^2-2$
$=(27)^2-2$
$=729-2$
$=727$
View full question & answer→Question 164 Marks
If $3 \mathrm{x}-\frac{1}{3 \mathrm{x}}=5$, find: $9 \mathrm{x}^2+\frac{1}{9 \mathrm{x}^2}$
Answer$ 9 x^2+\frac{1}{9 x^2}$
$=\left(3 x-\frac{1}{3 x}\right)^2+2$
$ =(5)^2+2$
$ =25+2$
$ =27$
View full question & answer→Question 174 Marks
If $2 a+\frac{1}{2 a}=8$, find : $16 a^4+\frac{1}{16 a^4} C$
Answer$ 16 a^4+\frac{1}{16 a^4}$
$=\left(4 a^2+\frac{1}{4 a^2}\right)^2-2.4 a^2 \cdot \frac{1}{4 a^2}$
$ =(62)^2-2$
$ =3844-2$
$ =3842$
View full question & answer→Question 184 Marks
If $2 \mathrm{a}+\frac{1}{2 \mathrm{a}}=8$, find $: 4 \mathrm{a}^2+\frac{1}{4 \mathrm{a}^2}$
Answer$ 4 a^2+\frac{1}{4 a^2}$
$=\left(2 a+\frac{1}{2 a}\right)^2-2.2 a \frac{1}{2 a}$
$ \left(2 a+\frac{1}{2 a}\right)^2-2$
$ =(8)^2-2$
$ =64-2$
$ =62$
View full question & answer→Question 194 Marks
If $a^2 + b^2 = 41$ and $ab = 4,$ find $: a + b$
Answer$(a + b)^2 = a^2 + b^2 + 2ab= 41 + 2(4)$
$= 41 + 8$
$= 49$
$\Rightarrow (a + b)^2 = 49$
$\therefore a + b = 7$
View full question & answer→Question 204 Marks
If $a^2 + b^2 = 41$ and $ab = 4,$ find $: a – b$
Answer$ (a-b)^2=a^2+b^2-2 a b$
$ =41-2(4)$
$ =41-8$
$ =33$
$\therefore a-b=\sqrt{33}$
View full question & answer→Question 214 Marks
If $\mathrm{m}-\frac{1}{\mathrm{~m}}=5$, find: $\mathrm{m}^2-\frac{1}{\mathrm{~m}^2}$
Answer$ \mathrm{m}^2-\frac{1}{\mathrm{~m}^2}$
$=\left(\mathrm{m}+\frac{1}{\mathrm{~m}}\right)\left(\mathrm{m}-\frac{1}{\mathrm{~m}}\right)$
$ =5\left(\mathrm{~m}+\frac{1}{\mathrm{~m}}\right)$
Now $\left(\mathrm{m}+\frac{1}{\mathrm{~m}}\right)^2=\left(\mathrm{m}-\frac{1}{\mathrm{~m}}\right)^2+4$
$ =(5)^2+4$
$ =25+4$
$ =29$
$ \therefore \mathrm{m}+\frac{1}{\mathrm{~m}}=\sqrt{29}$
$ \therefore \mathrm{m}^2-\frac{1}{\mathrm{~m}^2}=(5)(\sqrt{29})=5 \sqrt{29}$
View full question & answer→Question 224 Marks
If $\mathrm{m}-\frac{1}{\mathrm{~m}}=5$, find $: \mathrm{m}^4+\frac{1}{\mathrm{~m}^4}$
Answer$ m^4+\frac{1}{m^4}=\left(m^2+\frac{1}{m^2}\right)^2-2$
$ =(27)^2-2$
$ =729-2$
$ =727$
View full question & answer→Question 234 Marks
If $\mathrm{m}-\frac{1}{\mathrm{~m}}=5$, find $: \mathrm{m}^2+\frac{1}{\mathrm{~m}^2}$
Answer$ \mathrm{m}^2+\frac{1}{\mathrm{~m}^2}=\left(\mathrm{m}-\frac{1}{\mathrm{~m}}\right)^2+2$
$ =(5)^2+2$
$ =25+2$
$ =27$
View full question & answer→Question 244 Marks
If $a+\frac{1}{a}=2$, find : $a^4+\frac{1}{a^4}$
Answer$ a^4+\frac{1}{a^4}=\left(a^2+\frac{1}{a^2}\right)^2-2$
$ =(2)^2-2$
$ =4-2$
$ =2$
View full question & answer→Question 254 Marks
If $a+\frac{1}{a}=2$, find $: a^2+\frac{1}{a^2}$
Answer$ a^2+\frac{1}{a^2}=\left(a+\frac{1}{a}\right)^2-2$
$ =(2)^2-2$
$ =4-2$
$ =2$
View full question & answer→Question 264 Marks
Find the square of $9.7$
Answer$(9.7)^2 $
$= (10 − 0.3)^2= (10)^2 + (0.3)^2 − 2 (10) (0.3)$
$= 100 + 0.9 − 6$
$= 100.09 − 6.00$
$= 94.09$
View full question & answer→Question 274 Marks
Find the square of $391$
Answer$(319)^2$
$ = (400 − 9)^2= (400)^2 + 9^2 + 2 (400) (9)$
$= 160000 + 81 − 7200$
$= 152881$
View full question & answer→Question 284 Marks
Find the square of $607$
Answer$(607)^2 $
$= (600 + 7)^2= (600)^2 + (7)^2 + 2 (600) (7)$
$= 360000 + 49 + 8900$
$= 368449$
View full question & answer→Question 294 Marks
Find the square of $8 x+\frac{3}{2} y$
Answer$ \left(8 x+\frac{3}{2} y\right)^2$
$=(8 x)^2+\left(\frac{3}{2} y\right)^2+2 \times 8 x \times \frac{3}{2} y$
$ =64 x^2+\frac{9}{4} y^2+24 x y$
$ =64 x^2+24 x y+\frac{9}{4} y^2$
View full question & answer→Question 304 Marks
Find the square of $5 x+\frac{1}{5 x}$
Answer$ \left(5 \mathrm{x}+\frac{1}{5 \mathrm{x}}\right)^2$
$=(5 \mathrm{x})^2+\frac{1}{(5 \mathrm{x})^2}+2 \times 5 \mathrm{x} \times \frac{1}{5 \mathrm{x}}$
$ =25 \mathrm{x}^2+\frac{1}{25 \mathrm{x}^2}+2$
$ =25 \mathrm{x}^2+2+\frac{1}{25 \mathrm{x}^2}$
View full question & answer→Question 314 Marks
Find the square of $2 m^2-\frac{2}{3} n^2$
Answer$ 2 m^2-\frac{2}{3} n^2$
$ \left(2 m^2-\frac{2}{3} n^2\right)^2=\left(2 m^2\right)^2+\left(\frac{2}{3} n^2\right)^2-2 \times 2 m^2 \times \frac{2}{3} n^2$
$ =4 m^4+\frac{4}{9} n^4-\frac{8}{3} m^2 n^2$
$ =4 m^4-\frac{8}{3} m^2 n^2+\frac{4}{9} n^2$
View full question & answer→Question 324 Marks
Find the square of $\frac{5 a}{6 b}-\frac{6 b}{5 a}$
Answer$ \left(\frac{5 \mathrm{a}}{6 \mathrm{~b}}-\frac{6 \mathrm{~b}}{5 \mathrm{a}}\right)^2$
$=\left(\frac{5 \mathrm{a}}{6 \mathrm{~b}}\right)^2+\left(\frac{6 \mathrm{~b}}{5 \mathrm{a}}\right)^2-2 \times \frac{5 \mathrm{a}}{6 \mathrm{~b}} \times \frac{6 \mathrm{~b}}{5 \mathrm{a}}$
$ =\frac{25 \mathrm{a}^2}{36 \mathrm{a}^2}-2+\frac{36 \mathrm{~b}^3}{25 \mathrm{a}^2}$
View full question & answer→Question 334 Marks
Find the square of $3 x+\frac{2}{y}$
Answer$ 3 x+\frac{2}{y}$
$ \left(3 x+\frac{2}{y}\right)^2=(3 x)^2+\left(\frac{2}{y}\right)^2+2(3 x)\left(\frac{2}{y}\right)$
$ =9 x^2+\frac{4}{y^2}+\frac{12 x}{y}$
View full question & answer→Question 344 Marks
Evaluate : $203 \times 197$
Answer$ 203 \times 197$
$= (200 + 3) (200 − 3)$
$= (200)^2− (3)^2 ......[ \because (a − b) (a + b) = a^2 − b^2]$
$= 40000 − 9$
$= 39991$
View full question & answer→Question 354 Marks
Evaluate: $20.8 \times 19.2$
Answer$ 20.8 \times 19.2$
$= (20 + 0.8) (20 − 0.8)$
$= (20)^2− (0.8)^2 ......[ \because (a − b) (a + b) = a^2 − b^2]$
$= 400 − 0.64$
$= 399.36$
View full question & answer→Question 364 Marks
Evaluate : $(a + bc) (a − bc) (a^2 + b^2c^2)$
Answer$(a + bc) (a − bc) (a^2 + b^2c^2)$
$= [a^2 − (bc)^2] (a^2 + b^2c^2) .......[ \because (a − b) (a + b) = a^2 − b^2]$
$= (a^2 − b^2c^2) (a^2+ b^2c^2)$
$= (a^2)^2 − (b^2c^2)^2 .......[ \because (a − b) (a + b) = a^2 − b^2]$
$= a^4 − b^4c^4$
View full question & answer→Question 374 Marks
Evaluate : $(3x + 4y) (3x − 4y) (9x^2 + 16y^2)$
Answer$(3x + 4y) (3x − 4y) (9x^2 + 16y^2)$
$= [(3x)^2 − (4y)^2] (9x^2 + 16y^2) .....[ \because (a − b) (a + b) = a^2 − b^2]$
$= (9x^2 − 16y^2) (9x^2 + 16y^2)$
$= (9x^2)^2 − (16y^2)^2 ......[ \because (a − b) (a + b) = a^2− b^2]$
$= 81x^4 − 256y^4$
View full question & answer→Question 384 Marks
Evaluate: $(m + 3) (m − 3) (m^2 + 9)$
Answer$(m + 3) (m − 3) (m^2 + 9)$
$= (m)^2− (3)^2 (m^2 + 9) ......[ \because (a − b) (a + b) = a^2 − b^2]$
$= (m^2− 9) (m^2 + 9)$
$= (m^2)^2− 9^2$
$= m^4− 81$
View full question & answer→Question 394 Marks
Evaluate: $(1.6x + 0.7y) (1.6x − 0.7y)$
Answer$(1.6x + 0.7y) (1.6x − 0.7y)$
$= (1.6x)^2 − (0.7y)^2......[ \because (a − b) (a +b) = a^2 − b^2]$
$= 2.56x^2 − 0.49y^2$
View full question & answer→Question 404 Marks
Evaluate : $(4x^2 − 5y^2) (4x^2 + 5y^2)$
Answer$(4x^2 − 5y^2) (4x^2 + 5y^2)$
$= (4x)^2 − (5y^2)^{2 }$
$= 16x^4 − 25y^4 ......[ \because (a − b) (a + b) = a^2 − b^2]$
View full question & answer→Question 414 Marks
Evaluate: $\left(2 \mathrm{a}+\frac{1}{2 \mathrm{a}}\right)\left(2 \mathrm{a}-\frac{1}{2 \mathrm{a}}\right)$
Answer$ \left(2 a+\frac{1}{2 a}\right)\left(2 a-\frac{1}{2 a}\right)$
$ =(2 a)^2-\left(\frac{1}{2 a}\right)^2 \ldots \ldots .\left[\because(a-b)(a+b)=a^2 b^2\right]$
$ =4 a^2-\frac{1}{4 a^2}$
View full question & answer→Question 424 Marks
Evaluate : $(6 − 5xy) (6 + 5xy)$
Answer$(6 − 5xy) (6 + 5xy)$
$= (6)^2− (5xy)^2$
$= 36 − 25x^2y^2 .........[ \because (a − b) (a + b) = a^2b^2]$
View full question & answer→Question 434 Marks
Evaluate: $\left(\frac{4}{7} \mathrm{a}+\frac{3}{4} \mathrm{~b}\right)\left(\frac{4}{7} \mathrm{a}-\frac{3}{4} \mathrm{~b}\right)$
Answer$ \left(\frac{4}{7} a+\frac{3}{4} b\right)\left(\frac{4}{7} a-\frac{3}{4} b\right)$
$ =\left(\frac{4}{7} a\right)^2-\left(\frac{3}{4} b\right)^2 \ldots \ldots\left[\because(a-b)(a+b)=a^2 b^2\right]$
$ =\frac{16}{49} a^2-\frac{9}{16} b^2 S$
View full question & answer→Question 444 Marks
Evaluate: $\left(2 \mathrm{x}-\frac{3}{5}\right)\left(2 \mathrm{x}+\frac{3}{5}\right)$
Answer$ \left(2 \mathrm{x}-\frac{3}{5}\right)\left(2 \mathrm{x}+\frac{3}{5}\right)$
$ =(2 \mathrm{x})^2-\left(\frac{3}{5}\right)^2 \ldots \ldots .\left[\because(\mathrm{a}-\mathrm{b})(\mathrm{a}+\mathrm{b})=\mathrm{a}^2 \mathrm{~b}^2\right]$
$ =4 \mathrm{x}^2-\frac{9}{25}$
View full question & answer→Question 454 Marks
Evaluate: $(3a^2 − 4b^2) (8a^2 − 3b^2)$
Answer$(3a^2 − 4b^2) (8a^2 − 3b^2)$
$= 3a^2(8a^2 − 3b^2) − 4b^2 (8a^2 − 3b^2)$
$= 24a^4 − 9a^2b^2 − 32a^2b^2 + 12b^4$
$= 24a^{4 }− 41a^2b^2 + 12b^4$
View full question & answer→Question 464 Marks
Evaluate: $(5xy − 7) (7xy + 9)$
Answer$(5xy − 7) (7xy + 9)$
$ = 5xy (7xy + 9) − 7 (7xy + 9)= 35x^2y^2+ 45xy − 49xy − 63$
$= 35x^2y^2 − 4xy − 63$
View full question & answer→Question 474 Marks
The difference between the two numbers is $5$ and their products are $14.$ Find the difference between their cubes.
AnswerLet $x$ and $y$ be two numbers, then $x – y = 5$ and $xy = 14\therefore x^3 − y^3 = (x − y)^3 + 3xy(x − y)$
$= (5)^3 + 3 \times 14 \times 5$
$= 125 + 210$
$= 335$
View full question & answer→Question 484 Marks
Evaluate: $(4 − ab) (8 + ab)$
Answer$(4 − ab) (8 + ab) $
$= 4 (8 + ab) − ab (8 + ab)= 32 + 4ab − 8ab − a^2b^2$
$= 32 − 4ab − a^2b^2$
View full question & answer→Question 494 Marks
If $5x – 4y = 7$ and $xy = 8,$ find $: 125x^3 – 64y^3.$
Answer$125x^3 − 64y^3$
$ = (5x)^3 − (4y)^3= (5x − 4y)^3 + 3(5x) (4y) (5x − 4y)$
$= (5x − 4y)^3 + 60xy (5x − 4y)$
$= (7)^3+ 60 (8) (7)$
$= 343 + 3360$
$= 3703$
View full question & answer→Question 504 Marks
Evaluate : $(a^2 + 5) (a^2 − 3)$
Answer$(a^2 + 5) (a^2 − 3)$
$ = a^2 (a^2 − 3) + 5 (a^2 − 3)$
$= a^4− 3a^2 + 5a^2 − 15$
$= a^4 + 2a^2 − 15$
View full question & answer→